$\"\"$

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The equation is $\"x$ .

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Complete the squares.

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Add $\"\"$ to each side.

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$\"x$

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$\"x$

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Algebraic formula: $\"\"$ .

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$\"open$

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$\"\"$

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$\"\"$

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Compare equation with standard form of parabola equation $\"open$ and write the coefficients.

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Vertex $\"\"$ .

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Focus $\"\"$ is at $\"\"$ and

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Directrix line is $\"\"$ .

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Latus rectum is the line segment of a parabola perpendicular to axis which has both ends on the curve.

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The parabola equation is $\"open$ .

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Obtain the points define the latus rectum, let $\"\"$ .

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$\"\"$

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$\"open$

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$\"open$

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$\"x$

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$\"x$

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$\"x$

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The latus rectum points $\"\"$ and $\"\"$ .

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$\"\"$

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Graph :

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(1) Draw the coordinate plane.

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(2) Graph the parabola equation $\"open$ .

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(3) Plot the vertex, focus, and the two points $\"\"$ and $\"\"$ .

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(4) Draw the directrix line.

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(5) Connect the plotted points with smooth curve.

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$\"\"$

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$\"\"$

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The parabola equation is $\"open$ .

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The latus rectum points $\"\"$ and $\"\"$ .

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Graph of the parabola is

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$\"\"$ .